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Difficulty: MediumUS Customary Linear Measurements

A county maintenance crew is installing reflective markers along a newly paved road that is exactly 11 mile long. They completed the work over three days. On the first day, they marked 14\frac{1}{4} of a mile. On the second day, they marked 16\frac{1}{6} of a mile. On the third day, they marked a section measuring 300300 yards, 11 foot, and 88 inches. What is the length of the road that still needs markers, in feet and inches?

  1. 2,1782,178 feet and 44 inchesAnswer
  2. B
    3,3223,322 feet and 44 inches
  3. C
    2,9782,978 feet and 44 inches
  4. D
    2,7782,778 feet and 44 inches

Answer

The remaining length of the road that needs markers is 2,1782,178 feet and 44 inches.
To find the remaining distance, all measurements must be converted to a common unit (feet and inches). The total road is 5,2805,280 feet. The first two days account for 14×5,280=1,320\frac{1}{4} \times 5,280 = 1,320 feet and 16×5,280=880\frac{1}{6} \times 5,280 = 880 feet. The third day accounts for 300×3=900300 \times 3 = 900 feet, plus 11 foot and 88 inches, totaling 901901 feet 88 inches. The total completed is 1,320+880+901 ft 8 in=3,101 feet 8 inches1,320 + 880 + 901 \text{ ft } 8 \text{ in} = 3,101 \text{ feet } 8 \text{ inches}. Subtracting this from 5,2805,280 feet (written as 5,2795,279 feet 1212 inches for borrowing) leaves exactly 2,1782,178 feet and 44 inches.

Step-by-Step Solution

1
Convert the total road length from miles to feet.
1 mile=5,280 feet1 \text{ mile} = 5,280 \text{ feet}.
Establishing a standard unit (feet) is necessary to evaluate the remaining length accurately.
2
Calculate the exact distance completed on the first and second days in feet.
Day 1: 14×5,280=1,320 feet\frac{1}{4} \times 5,280 = 1,320 \text{ feet}. Day 2: 16×5,280=880 feet\frac{1}{6} \times 5,280 = 880 \text{ feet}.
Converting the fractional mile measurements into feet allows them to be added to the other measurements.
3
Convert the third day's distance entirely into feet and inches.
300 yards=300×3=900 feet300 \text{ yards} = 300 \times 3 = 900 \text{ feet}. Adding the rest: 900 ft+1 ft+8 in=901 feet 8 inches900 \text{ ft} + 1 \text{ ft} + 8 \text{ in} = 901 \text{ feet } 8 \text{ inches}.
All components of the third day's work must be in the common feet/inches format to find the total sum.
4
Sum the completed distances from all three days.
1,320 ft+880 ft+901 ft 8 in=3,101 feet 8 inches1,320 \text{ ft} + 880 \text{ ft} + 901 \text{ ft } 8 \text{ in} = 3,101 \text{ feet } 8 \text{ inches}.
This provides the total length of the road that has already been marked.
5
Subtract the total completed distance from the total road length.
5,280 ft 0 in−3,101 ft 8 in5,280 \text{ ft } 0 \text{ in} - 3,101 \text{ ft } 8 \text{ in}. Borrow 11 foot (1212 inches): 5,279 ft 12 in−3,101 ft 8 in=2,178 feet 4 inches5,279 \text{ ft } 12 \text{ in} - 3,101 \text{ ft } 8 \text{ in} = 2,178 \text{ feet } 4 \text{ inches}.
Subtracting the completed work from the total length yields the final remaining measurement required.

Key Concept

Multi-step conversion between US customary linear units (miles, yards, feet, inches) and fraction operations.
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Topics

US Customary Linear Measurements

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